They have set a deadline of Sunday evening, with the option of extending into Monday or Tuesday.
On the agenda are detailed questions about how a repeat of the "grand coalition" or "GroKo" that has ruled since 2013 will shape healthcare, labour law, pensions and reform of the European Union and euro single currency.
Both sides are reluctant to compromise too much and risk losing support, but are equally fearful of going back to voters in repeat elections that could see a further rise of the far-right.
"I hope we can manage it," Merkel said Friday, warning however that there were still "a whole list of very serious points of disagreement".
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At stake for Merkel -- still rated a "good" or "very good" choice for chancellor by 51 percent of respondents to the same poll -- is whether she leads a stable coalition into her fourth term, or risks a fragile minority government or new elections.
Social Democrats agreed to talks only after Merkel's soundings with two smaller parties, the ecologist Greens and the pro-business Free Democrats, fell through.
Challenged by rebels within his own ranks, SPD leader Martin Schulz has sought political cover by putting any final coalition deal to a vote by all 440,000 members.
Kevin Kuehnert, leader of the SPD youth wing, has become a standard bearer for opponents of a new deal with Merkel.
"This kind of politics was rewarded with a 14 percentage point drop (for CDU and SPD combined) last year, and I suspect things will continue that way" if the coalition materialises, he has said.
Merkel too faces grumbling among her troops, with more conservative voices accusing her of marching her Christian Democratic Union (CDU) too far into the political centre, giving up terrain to the AfD.
Meanwhile, the press has scented the end of an era approaching.
Eight years of GroKo under Merkel -- from 2005-09 and again from 2013-17 -- had shown that "the lowest common denominator achieves nothing as long as there is no overarching idea," commented Stefan Braun for the Sueddeutsche Zeitung.
Merkel and Schulz should offer honest, ambitious answers to the country's big challenges or "leave the way clear for new leaders or new elections".